摘要
We study the stability of unduloids with free boundary in the domain B between two parallel hyperplanes in R^(n+1). If the unduloid has one half of period in B and is sufficiently close to a cylinder, then for 2≤n≤10, it is unstable; while for n≥11, it is stable. If the unduloid has two or more halves of period in B and is sufficiently close to a cylinder, then for all n≥2, it is unstable.
We study the stability of unduloids with free boundary in the domain B between two parallel hyperplanes in R^（n＋1）. If the unduloid has one half of period in B and is sufficiently close to a cylinder, then for 2≤n≤10, it is unstable; while for n≥11, it is stable. If the unduloid has two or more halves of period in B and is sufficiently close to a cylinder, then for all n≥2, it is unstable.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11271214 and 11671224)
Ben Andrews’ ARC Laureate Fellowship (Grant No. FL150100126)
